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Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34 Page 9 of 14

indicating that they are potential HER catalysts. Supplementary Figure 8 depicts the calculated exchange
currents for the above catalyst models based on their adsorption free energies. Among them, CoN -gra,
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NiNiN -gra, FeNiN -gra, CoNi-N -gra, FeFeN -gra, and FeCoN -gra reside much closer to the volcano peak
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with high activity.
Origins of HER activity
The above calculation results show that CoN -gra, NiNiN -gra, CoNiN -gra, and MMN -gra/M1M2N -gra
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all have better activities for catalyzing HER. However, the underlying reasons for their enhanced activities
may be different.
For CoN -gra, its excellent HER activity can be attributed to the moderate adsorption of H on Co sites. To
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understand the huge difference in the H adsorption capacity of different metal sites, the charge transfer
between metal atoms as HER active sites and adsorbed hydrogen atoms was further investigated. The charge
density difference shows that charge accumulation (yellow area) mainly occurs on the adsorbed H atoms,
whereas charge depletion (cyan area) is concentrated around the metal atoms [Supplementary Figure 9]. In
addition, the results of Bader charge analysis show that the adsorption free energy of H increases with the
decrease of the negative charge it carries; that is, the adsorption gradually weakens. For example, the
negative charges carried by H on CoN -gra and CoCoN -gra are -0.07 and -0.03 [Figure 6A and B],
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respectively, and the adsorption free energies of H are correspondingly 0.19 and 0.84 eV.
The COHP between the metal atoms and the adsorbed H atoms was further calculated [Supplementary
Figure 10]. The activation of H was also quantitatively assessed using the ICOHP. In general, a more
negative ICOHP corresponds to a stronger H adsorption. For example, the Co-H interaction in CoN -gra
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(ICOHP: -3.28, Figure 6C) is much stronger than that in CoCoN -gra (ICOHP: -3.08, Figure 6D). A clear
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linear correlation between the ICOHP of M-H and the free energy of H adsorption for all MN -gra/
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MMN -gra/M1M2N -gra can be found in Figure 7A. This is also consistent with the above analyses that the
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downshifted d-band center of Co atoms in CoCoN -gra leads to the decreased H adsorption capacity of Co
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sites [Supplementary Table 10]. The DOS results also show slightly more obvious hybridization between the
states of CoN -gra and adsorbed hydrogen [Figure 6C and D]. In addition, Figure 7B also plots the linear
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relationship between the metal d-band center and the H adsorption free energy, and the adsorption capacity
of the metal site for H is in good agreement with the change of the d-band center.
The enhanced H adsorption capacity of MMN -gra/M1M2N -gra is consistent with the reduced
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coordination number and upshifted d-band center of the central metal [Supplementary Figure 5 and
Supplementary Table 10]. Besides, the bridge site between two metals of MMN -gra/M1M2N -gra also helps
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to enhance their capture abilities. Further charge density difference and Bader charge analyses revealed that
both metal atoms on MMN -gra/M1M2N -gra transfer electrons to the adsorbed H atoms, which results in
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a significant increase in the amount of charge on H (≤ -0.15, Figure 8) compared to the less negative charge
of H on MMN -gra/M1M2N -gra (≥ -0.11, Supplementary Figure 9). In addition, according to the COHP
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analyses [Supplementary Figure 11], the bimetallic atoms on MMN -gra/M1M2N -gra simultaneously have
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bonding interactions with the adsorbed H atoms. This further confirms that the dual atoms in MMN -gra/
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M1M2N -gra both contribute to the H adsorption. Meanwhile, the excellent HER activity of MMN -gra/
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M1M2N -gra to generate H through HMH intermediates can also be attributed to the enhancement of H
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adsorption capacity after reducing the coordination number of metal active centers and the synergistic effect
of bimetallic site on H adsorption.